Scholarlink

<p>Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(R=K[x_1,\ldots , x_n]\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <mo>=</mo> <mi>K</mi> <mo stretchy="false">[</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>x</mi> <mi>n</mi> </msub> <mo stretchy="false">]</mo> </mrow> </math></EquationSource> </InlineEquation> be the polynomial ring in <i>n</i> variables over a field <i>K</i>, and let <i>I</i> be a monomial ideal of <i>R</i>. In this short note, we show that if <i>I</i> is of Veronese-type, then for all positive integers <i>k</i>, the powers <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(I^k\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>I</mi> <mi>k</mi> </msup> </math></EquationSource> </InlineEquation> and the radical <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\sqrt{I}\)</EquationSource> <EquationSource Format="MATHML"><math> <msqrt> <mi>I</mi> </msqrt> </math></EquationSource> </InlineEquation> are sequentially Cohen-Macaulay.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

A note on sequentially Cohen-Macaulay Veronese-type monomial ideal

  • 期刊论文

  • 发表日期：

    2026年7月4日

查看全文
  • Amir Mafi,
  • Dler Naderi

摘要

Let \(R=K[x_1,\ldots , x_n]\) R = K [ x 1 , … , x n ] be the polynomial ring in n variables over a field K, and let I be a monomial ideal of R. In this short note, we show that if I is of Veronese-type, then for all positive integers k, the powers \(I^k\) I k and the radical \(\sqrt{I}\) I are sequentially Cohen-Macaulay.